HemoDyn

Physiological-Model Informed Neural Networks (PMINNS) of Hemodynamics

PMINNs Concept

A new methodology is proposed and called Physiological Model-Informed Neural Networks (PMINNs), where a physiologically grounded model serves as a compact and interpretable architecture. Like traditional neural networks, PMINNs learn from data—but instead of learning abstract weights in a black-box, they estimate undetermined physiological parameters embedded within a mechanistic structure. This hybrid approach combines the interpretability of physiological models with the adaptability of machine learning.

PMINNs Procedure

Step 1 – Model Generalization

• Begin with a validated physiological model.
• Perform sensitivity analysis to identify the most influential parameters.
• Generalize the model by introducing variability (unknowns).

Step 2 – Learning Process

• Construct a learning pipeline similar to neural networks:
• Define a loss function (e.g., mean squared error between model outputs and biomedical measurements).
• Apply gradient-based optimization or probabilistic learning to estimate the unknown parameters.
• Incorporate regularization informed by physiological constraints.

Step 3 – Interpretation

• Translate the trained parameters back into physiologically meaningful values.
• Assess generalization using cross-validation or domain-specific validation (e.g., physiological plausibility, expert review).

Analogy to Neural Networks

Neural Networks	PMINNs
Layers	Model components (e.g., chambers, vessels, membranes and muscles)
Nodes	Physiological factors
Weights	Factor weights
Activations	Mechanistic responses
Training	Fitting model outputs to data

Comparative Analysis: PMINNs vs. PINNs

Physiological Model-Informed Neural Networks (PMINNs) introduce a structured, interpretable approach to learning from biomedical data. Compared to Physics-Informed Neural Networks (PINNs), PMINNs offer advantages in transparency and practical implementation for physiological systems.

Model Structure and Interpretability

PINNs embed physical laws such as PDEs into neural network loss functions. While physics is respected, the network's weights are still black-box parameters. Interpretability is limited.

PMINNs, in contrast, retain a physiological model structure with clearly defined parameters. These parameters are directly interpretable in medical terms, enhancing model trust and clinical relevance.

Data Requirements and Training Efficiency

PINNs may require large datasets and careful balancing of data and physics losses, often resulting in complex optimization dynamics.

PMINNs leverage known physiological structures, enabling more efficient learning with smaller datasets and faster convergence.

Application Scope

PINNs have broad applicability across physics domains but need extensive adaptation for medical-specific scenarios.

PMINNs are tailored to physiological systems, making them ideal for clinical applications, digital health, and personalized medicine.

Summary Table

Feature	PINNs	PMINNs
Integration Approach	Physics laws in loss function	Physiological models in architecture
Interpretability	Low	High
Data Requirements	High	Moderate to Low
Training Efficiency	Variable	Potentially Higher
Application Domains	General physical systems	Biomedical and physiological systems

Why is PMINNs necessary and how to implement specifically?

Traditional approaches to analyzing vascular diseases face a fundamental trade-off between statistical correlation methods and machine learning techniques. While neural networks offer powerful pattern recognition capabilities, they typically require extensive training data and suffer from interpretability challenges. Physiological-model informed neural networks (PMINNs) present an alternative approach that combines the transparency of physiological models with the adaptability of machine learning.

It's natural for some to question the leap from industrial CFD to biological fluid dynamics. However, industrial CFD primarily involves forward simulations aimed at predicting fluid flow at specific moments, necessitating high computational accuracy. In contrast, biological fluid dynamics focuses on constructing logical frameworks of information flow.

For instance, modeling blood oxygen transport requires considering frictional transport within vessels, transmembrane flux influenced by pressure differences, diffusion into muscle tissue, and metabolic consumption. My algorithm encapsulates the entire process from the heart to muscles, forming a parameterized expression linking inputs to outputs.

The reliability of this model is comparable to that of neural networks; both serve as foundational models for machine learning. These models are tools for method and process, not end products. In regression analysis, choosing between linear or nonlinear models doesn't solely determine the quality of the regression curve. Similarly, machine learning is essentially a form of regression and a branch of mathematical optimization.

In data-driven applications, the simulation process is inverse, aiming to find the most "adequate" model—a parameterized physiological logic framework. After extensive data training, this model can assess the effectiveness of medical interventions. Its significance lies in requiring fewer samples and providing rapid identification.

Stanford University has released the world's only open-source hemodynamic model, sparking a surge of interest among algorithm pioneers. With over thirty years of experience in fluid algorithm research, particularly in numerical model forecasting, and recent years in CAE algorithm development, I bring a unique perspective to applying hemodynamic models in digital health.

The HemoDyn platform implements a hybrid architecture that integrates:

• 1D Reduced-Order Hemodynamics Solver: Based on SimVascular's ROM framework for efficient arterial blood flow modeling
• Oxygen Transport Simulation: Implemented with Elmer Multiphysics to capture oxygen delivery, exchange, and muscular consumption dynamics
• Wearable Data Integration: Real-time pulse data from smartwatches and oximeters provide continuous physiological inputs
• Machine Learning Layer: Neural networks trained on clinical outcomes parameterize physiological uncertainties while maintaining biological constraints

This architecture offers several methodological advantages:

• Network nodes represent physiological mechanisms rather than abstract mathematical constructs
• Predictions maintain interpretability through direct mapping to biological processes
• Combination of measured signals and physics-informed structure reduces uncertainty

Implementation Framework

The HemoDyn implementation follows a structured workflow:

1. Simplified anatomical modeling of lower extremity vasculature and muscle tissue
2. Mesh generation using Gmsh with conversion via ElmerGrid
3. Configuration of ElmerSolver components (ModelPDE, HeatSolve)
4. Execution of SimVascular ROM and ElmerSolver processes
5. Visualization of results through VTK pipelines
6. Development of interactive controls for vascular parameter exploration

Simulation Demonstrations

The following videos demonstrate HemoDyn's hemodynamic simulation capabilities and user interface:

User Interface Overview

Blood Flow Dynamics

Microvasculature-tissue level simulation

Clinical Applications and Future Directions

HemoDyn demonstrates particular promise in addressing Lower Extremity Arterial Occlusive Disease (LEAO), a condition affecting approximately 12% of individuals aged 65 and rising to 50% prevalence in those over 80. Current clinical challenges include:

• Difficulty in short-term evaluation of therapeutic interventions
• Lack of quantitative metrics for treatment efficacy assessment
• High variability in individual physiological responses

The platform's closed-loop integration with wearable devices enables:

• Continuous monitoring of pulse and blood oxygen metrics
• Automated collection of resting and post-exercise physiological data
• Cloud-based analysis with real-time feedback on treatment trends

Future development pathways include:

• Extension to chronic disease monitoring applications
• Integration with electronic health records for enriched modeling
• Development of drug efficacy evaluation frameworks

Vision and Collaboration

Current digital health technologies primarily identify health conditions through data on breathing, wrist pulse, and limb movement, with neural networks serving as the algorithmic models between input and output, rarely incorporating physiological models. Even when they do, the models are simplified to near insignificance due to traditional physiological models' bottlenecks—inaccuracy and slowness. Breakthrough algorithms must be fast while capable of incorporating physiological logic.

On LinkedIn, I posed the following thought-provoking question as part of my research methodology: "Is there a CFD application scenario worth attempting that hasn't been tried before, describable in one sentence?" I believe "In clinical trial design, hemodynamic CFD could help reduce sample sizes, thereby shortening trial cycles and lowering pharmaceutical development costs" qualifies as one, as literature shows no reports of hemodynamic CFD being used to reduce clinical trial sample sizes.

If you argue it's not worth attempting, please consider these two brief questions:

If knowledge gaps must be addressed with machine learning, would you prefer traditional neural network models or physiologically constrained models. The latter is also NN, but with fewer unknown nodes networked up with physiological mechanism.

For CFD to have practical impact on human health, how should computational resources be balanced between physiology representation and numerical precision?

Through professional discussions on these questions, I've strengthened my conviction. Since then, I've proceeded with algorithm design planning and programming implementation. This webpage contains all publicly available materials.

As the algorithm developer, I now seek to connect with product developers for collaboration.